Advanced optical designs for imaging systems

ABSTRACT

An eye-mounted device includes a contact lens and an embedded imaging system. The front aperture of the imaging system faces away from the user&#39;s eye so that the image sensor in the imaging system detects imagery of a user&#39;s external environment. The optics for the imaging system has a folded optical path, which is advantageous for fitting the imaging system into the limited space within the contact lens. In one design, the optics for the imaging system is based on a two mirror design, with a concave mirror followed by a convex mirror.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a continuation-in-part of U.S. patent applicationSer. No. 16/895,077, “Advanced Optical Designs for Eye-mounted ImagingSystems,” filed Jun. 8, 2020; which is a continuation-in-part of U.S.patent application Ser. No. 16/034,761 now U.S. Pat. No. 10,712,564,“Advanced Optical Designs for Eye-Mounted Imaging Systems,” filed Jul.13, 2018. The subject matter of all of the foregoing is incorporatedherein by reference in its entirety.

BACKGROUND 1. Technical Field

This disclosure relates generally to imaging optics, for example as maybe used with an eye-mounted imaging system.

2. Description of Related Art

Handheld cameras are ubiquitous. A large fraction of the world'spopulation carries smartphones and most smartphones have one or morecameras. This allows people to document their lives and experiences.Pictures and videos of epic events, spectacular vacations and lifetimemilestones are routinely captured by handheld cameras. At the other endof the spectrum, the number of selfies, cat videos and pictures ofmediocre meals has also exploded in recent years.

Body-mounted cameras or body-cams go one step further. Theyautomatically go where the user goes and can automatically record whatthe user is experiencing. Head-mounted or helmet-mounted cameras go evenone step further. They automatically view what the user is viewing or,at least where he turns his head. They can record events from this pointof view.

However, all of these imaging devices are separate pieces of equipmentthat are visible to others. They are also relatively large and are notcarried on the user's eye.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure have other advantages and features whichwill be more readily apparent from the following detailed descriptionand the appended claims, when taken in conjunction with the examples inthe accompanying drawings, in which:

FIG. 1A shows a user wearing an eye-mounted device in communication withan auxiliary necklace.

FIG. 1B shows a magnified view of the electronic contact lens mounted onthe user's eye.

FIG. 2 shows a cross sectional view of an electronic contact lens withan embedded imaging device (femtoimager).

FIGS. 3A-3C show cross sectional views of a femtoimager optical system,with possible ray paths to the center, right edge and left edge of theimage sensor, respectively.

FIGS. 4A and 4B show perspective views of a femtoimager optical system.

FIG. 5 shows a cross sectional view of an eye-mounted device with afemtoimager and a femtoprojector.

FIG. 6 shows a cross sectional view of another femtoimager opticalsystem.

FIG. 7 shows a cross sectional view of yet another femtoimager opticalsystem.

FIG. 8 shows a cross sectional view of a horizontally positionedfemtoimager in a contact lens.

FIG. 9 shows a cross sectional view of yet another femtoimager in acontact lens.

FIG. 10A shows a cross-sectional view of yet another femtoimager, withpossible ray paths to the left edge, center and right edge of the imagesensor.

FIG. 10B shows extraneous rays blocked by baffles in the femtoscope ofFIG. 10A.

FIG. 11A shows a cross-sectional view of yet another femtoimager.

FIG. 11B shows reflected extraneous rays blocked by baffles in thefemtoscope of FIG. 11A.

FIGS. 12-15 show cross-sectional views of additional femtoimagers.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The figures and the following description relate to embodiments by wayof illustration only. It should be noted that from the followingdiscussion, alternative embodiments of the structures and methodsdisclosed herein will be readily recognized as viable alternatives thatmay be employed without departing from the principles of what isclaimed.

An eye-mounted device includes a contact lens and an embedded imagingdevice, which for convenience is referred to as a femtoimager because itis very small. The front aperture of the femtoimager faces away from theuser's eye so that the image sensor in the femtoimager captures imageryof a user's external environment. In various embodiments, thefemtoimager operates in a visible wavelength band, a non-visiblewavelength band, or a combination of both.

The femtoimager optics has a folded optical path, which is advantageousfor fitting the femtoimager into the limited space within the contactlens. In one design, the optics for the femtoimager is a two mirrordesign, with a concave primary mirror followed by a convex secondarymirror in the optical path from the front aperture to the image sensor.In some embodiments, the optical system includes a solid transparentsubstrate with the primary mirror formed on one face of the substrateand the secondary mirror formed on an opposing face of the substrate.The front aperture is annular and may be axially positioned between thetwo mirrors. It may include a lens or other refractive interface. Lightblocking structures, light-redirecting structures, absorbing coatingsand other types of baffle structures are used to reduce or eliminateextraneous light from reaching the image sensor.

The eye-mounted device may include other components in the contact lens:a projector that projects images onto the retina, other types ofsensors, electronics, batteries, a coil to wirelessly receive power, oran antenna to transmit/receive data, for example. These components maybe positioned in front of the pupil in the optical path of the eye. Somecomponents must be positioned within this optical zone, for example inorder to project images onto the retina. Other components may bepositioned outside the optical zone. The femtoimager may be eitherwithin or outside the optical zone.

In more detail, FIG. 1A shows a user wearing an eye-mounted device 105in communication with a necklace 106. FIG. 1B shows a magnified view ofthe user's eye and eye-mounted device. The eye-mounted device 105includes a contact lens 110 that is worn on the surface of the eye. Thefollowing examples use a scleral contact lens but the contact lens doesnot have to be scleral. The contact lens 110 contains a femtoimager 120.The femtoimager 120 captures images of the external environment.

FIG. 1B shows a front view of the contact lens 110 mounted on a user'seye. The contact lens 110 is placed on the surface of the eye. Thecontact lens 110 moves with the user's eye as the user's eye rotates inits socket. Because the femtoimager 120 is mounted in the contact lens110, it also moves with the user's eye. The ratio of the contact lensdiameter to femtoimager lateral size is preferably roughly 15:1. Thisratio is normally between about 15:1 and 30:1, but may be as small as5:1 or smaller or as large as 50:1 or larger.

In this example, the contact lens 110 also contains electronics 140 anda coil (or antenna) 145. In some embodiments, the coil 145 is a powercoil that receives power wirelessly, for example via magnetic induction.In other embodiments, the contact lens 110 includes a battery thatsupplies power to the femtoimager 120. The electronics 140 may be usedto control the femtoimager, receive or process images from thefemtoimager, provide power to the femtoimager, and/or transmit datato/from the femtoimager. The contact lens 110 may also include othercomponents, such as a projector that projects images onto the user'sretina (referred to as a femtoprojector).

FIG. 1A shows an implementation where, in addition to the eye-mounteddevice 105, the user is also wearing a necklace 106 that containscomponents of the eye-mounted system. In this example, the necklace 106includes a wireless transceiver 107 that transmits/receives image dataand/or transmits power to the eye-mounted device 105. Image transmissionto/from an eye-mounted device is subject to data rate constraints due tosize and power consumption limitations of electronics in a contact lens.Off-lens accessory devices may be used in place of, or in addition to, anecklace.

FIG. 2 shows a cross sectional view of the contact lens 110 withembedded femtoimager 120. FIG. 2 shows an embodiment using a scleralcontact lens but the contact lens 110 does not have to be scleral. Thecontact lens 110 preferably has a thickness that is less than two mm.The femtoimager 120 preferably fits in a 1 mm×1 mm×1 mm volume, or atleast within a 2 mm×2 mm×2 mm volume. The contact lens 110 iscomfortable to wear and maintains eye health by permitting oxygen toreach the cornea 150.

For completeness, FIG. 2 shows some of the structure of the eye 100. Thecontact lens 110 is separated from the cornea 150 of the user's eye 100by a tear layer. The aqueous of the eyeball is located between thecornea and the crystalline lens 160 of the eye 100. The vitreous fillsmost of the eyeball. The iris 180 limits the aperture of the eye.

The femtoimager 120 is outward-facing, meaning the femtoimager 120“looks” away from the eye 100 and captures imagery of the surroundingenvironment. The field of view 125 of the femtoimager 110 may be thesame, smaller or larger than a field of view of the user's eye. As shownin more detail below, the femtoimager 110 includes imaging optics(referred to as a femtoscope), a sensor array and sensor circuitry. Thesensor array may be an array of photodiodes. In some embodiments, thesensor array operates in a visible wavelength band (i.e., ˜390 nm to 770nm). Alternatively or additionally, the sensor array operates in anon-visible wavelength band, such as an infrared (IR) band (i.e., ˜750nm to 10 μm) or an ultraviolet band (i.e., <390 nm). For example, thesensor array may be a thermal infrared sensor.

The sensor circuitry senses and conditions sensor signals produced bythe sensor array. In some instances, the output signals produced by thesensor circuitry are analog signals. Alternatively, the sensor circuitrymay include analog-to-digital converters (ADC), so that the outputsignals are digital rather than analog. The sensor circuitry may alsohave other functions. For example, the sensor circuitry may amplify thesensor signals, convert them from current to voltage signals or filternoise from the sensor signals to keep a signal-to-noise ratio below athreshold value. The sensor circuitry may be implemented as a separateelectronics module 140. Alternatively, it may be implemented as abackplane to the sensor array. Processing of the images captured by thefemtoimager may occur outside the contact lens 110.

FIGS. 3-4 show an example femtoimager design. FIGS. 3 and 4 show crosssectional views and perspective views, respectively, of a femtoimager.The femtoimager uses a femtoscope with two mirrors that direct incominglight to an image sensor 340. The femtoscope of FIG. 3 includes a solid,transparent substrate 310. The solid transparent substrate 310 may bemade from plastic, glass or other transparent materials. The femtoscopealso includes an annular concave primary mirror 360 and a convexsecondary mirror 350. Either or both of these may be aspheric. Theconcave primary mirror 360 may be formed by coating an end of thesubstrate 310 with a reflective material such as a metal (e.g. aluminumor silver) or an engineered stack of dielectric layers. The shape of theprimary mirror 360 may be made by any of several different techniques.For example, if the substrate is injection-molded plastic, then theshape of the primary mirror 360 follows the shape of the mold used.Alternatively, the shape of the primary mirror 360 may be made bydiamond turning the substrate on a lathe. Or, the shape of the primarymirror 360 may be made by photolithography and etching steps. Gray scalephotolithography may be used to etch a mirror surface profile, forexample. Wafer scale optics techniques including embossing, compressionmolding and/or UV curing photosensitive polymers may also be used toform mirror profiles. Additive manufacturing or three-dimensionalprinting (e.g. via two-photon polymerization) techniques may also beemployed. These techniques may also be used to form the secondary mirror350.

The primary mirror 360 includes a clear, non-reflective back aperture365 (also referred to as the output aperture). An image sensor 340, suchas an array of photodiodes, is mounted at this location. Other types ofimage sensors include phototransistors, CCDs, pyrometer-based sensors,micro-bolometers, and sensors based on vanadium oxide, silicon, indiumphosphide, gallium antimonide or gallium arsenide, for example.

The secondary mirror 350 faces the primary mirror 360, and the imagesensor 340 faces the secondary mirror 350. Light rays enter thefemtoscope through the front aperture 370 (also referred to as the inputaperture). They are first incident on and reflected by the annularprimary mirror 360. The reflected rays are then incident on and furtherreflected by the secondary mirror 350 before exiting through the backaperture 365 and reaching the image sensor 340. The primary mirror 360and secondary mirror 350 cooperate to form an image of the externalenvironment, which is captured by the image sensor 340.

The primary mirror 360 and secondary mirror 350 cooperate to image raysentering through the front aperture 370 onto the image sensor 340.However, not all light rays from the external environment are includedin image formation. Those light rays that are used to form an image arereferred to as image-forming rays. The remaining light rays are referredto as extraneous rays. In FIG. 3, the front aperture 370 is annular inshape (but not required to be planar). It is defined by an inner edge372 and outer edge 374. The front aperture 370 limits which rays enterthe optical system to form the image. In this design, the front aperture370 is not axially aligned with either of the mirrors 350, 360. That is,the z-coordinate of the front aperture 370 is between that of theprimary mirror 360 and the secondary mirror 350. In FIG. 3, the frontaperture 370 is located approximately midway between the two mirrors350, 360.

The system also includes a light baffle system to block or at leastreduce extraneous light. In FIG. 3, the baffle system includes an innerbaffle 382 which serves as a three-dimensional obscuration, and a sidebaffle with an external portion 384 and an internal portion 386. Thebaffles may be either an integral part of the femtoscope or asurrounding structure in which the optical system is mounted. Absorbingor black baffles may also make the femtoimager less visible to others.In one implementation, the obscuration 382 and internal side baffle 386are made by depositing an absorbing material such as carbon, roughenedor etched nickel (“nickel black”), black chrome, or Vantablack (SurreyNanoSystems, Newhaven, UK) on the transparent substrate 310, whichserves as the core of the optical system. Black indium-tin oxide mayalso be used. The external side baffle 384 may be separate from thesubstrate 310, for example, it may be an absorbing material deposited onthe sides of a hole into which the core is inserted during assembly.

In FIG. 3, the baffle system is designed to block all extraneous raysthat would have a direct path from the external environment to the imagesensor 340. Accordingly, the obscuration 382 extends an entire lengthbetween the secondary mirror 350 and the inner edge 372 of the frontaperture. The external side baffle 384 extends from the outer edge 374of the front aperture away from the primary mirror 360 and issufficiently long to block all extraneous rays that would propagatethrough the front aperture 370 directly to the image sensor 340.Although not required in FIG. 3, it may be extended to an edge that isaxially aligned with the secondary mirror 350 without adding length tothe overall system. The internal side baffle 386 extends an entirelength from the outer edge 374 of the front aperture to the primarymirror 360. In other embodiments, the baffle system may block less thanall of the extraneous rays, so the baffles may be shorter.

FIG. 3A shows possible ray paths to the center point of the image sensor340. These ray paths may be classified as follows. The bundle of rays341 are reflected by the primary mirror 360 and the secondary mirror 350to form the image on the image sensor 340. These are the image-formingrays 341. In FIG. 3A, the image-forming ray bundle 341 is labelled bothas it enters through the front aperture 370 and as it propagates fromthe secondary mirror 350 to the image sensor 340.

The remaining paths are possible paths for extraneous rays, which aremanaged as follows. Extraneous rays that might have propagated along theray paths in bundle 345 to the image sensor 340 are blocked by the backside of the secondary mirror 350. Extraneous rays are prevented fromreaching the possible ray paths in bundle 346 (between the solid ray andthe dashed ray) by the obscuration 382 and secondary mirror 350.Extraneous rays are prevented from reaching the possible ray paths inbundle 347 (between two dashed rays) by the external side baffle 384.The possible ray paths in bundle 348 are blocked by the internal sidebaffle 386. For clarity, only the lefthand rays are marked in FIG. 3A,but a similar situation exists for the righthand rays. Similar diagramsmay also be produced for other points on the image sensor 340.

FIGS. 3B and 3C show possible ray paths to the two edge points of theimage sensor 340. The extraneous rays are managed in a similar fashionas described in FIG. 3A. The edge points of FIGS. 3B and 3C also lead tothe following considerations. Again, consider only the lefthand rays. InFIG. 3B, the external side baffle 384 is tapered outwards (or otherwiseshaped) from the outer edge 374 of the front aperture so that it doesnot block the outermost image-forming ray 341X. Ray 341X passes throughthe outer edge 374 of the front aperture and is incident on the farthestpoint of the image sensor 340. As a result, it is propagating at theoutermost angle of all image-forming rays. If external side baffle 384does not block ray 341X, it also will not block any of the otherimage-forming rays. In addition, as shown in FIG. 3C, the external sidebaffle 384 is long enough to prevent extraneous rays from reaching raypath 347A. Because ray path 347A passes through the inner edge 372 ofthe front aperture to the outermost edge of the image sensor 340, itwill intersect the side baffle 384 at the farthest possible axialdistance from the image sensor 340.

Also in FIG. 3C, the obstruction 382 and internal side baffle 386 areshaped so that they do not block either image-forming ray 341Y or 341Z.Ray 341Y passes through the inner edge 372 of the front aperture and isincident on the nearest point on the image sensor 340. As a result, itis propagating at the innermost angle of all image-forming rays. Ifobstruction 382 does not block ray 341Y, it also will not block any ofthe other image-forming rays. In FIG. 3, the three-dimensionalobstruction 382 is the combination of an annulus next to the secondarymirror 350 plus a conical frustum that extends the entire length betweenthe annulus and the inner edge 372 of the front aperture.

FIGS. 4A-4B show perspective views of the femtoscope from FIG. 3. FIG.4A shows just the coated substrate 310. The internal side baffle 386 iscylindrical in shape (i.e., the sides are parallel to the optical axisof the system). The obstruction 382 is a frustum plus a narrow annulus,which is adjacent to the secondary mirror 350. The front aperture 370 isthe transparent annulus between the internal side baffle 386 andthree-dimensional obstruction 382. In some designs, the front aperture370 has an axial location that is closer to midway between the primaryand secondary mirrors, than to either the primary mirror 360 or thesecondary mirror 350. For example, if z is the axial dimension and thetwo mirrors are located at z=0 mm and z=1 mm, then the front aperture islocated in the range 0.25 mm<z<0.75 mm. The primary mirror and the backaperture for the image sensor are on the back face of the substrate,which is not visible in FIG. 4A. FIG. 4B also shows the external sidebaffle 384.

As noted above, the design in FIGS. 3-4 blocks all extraneous rays thatwould propagate directly to the image sensor 340. However, this is notstrictly required. The different baffles 382, 384, 386 do not have toextend the entire lengths shown. They may be shorter in some designs.For example, the obstruction 382 may occupy some of the space betweenthe secondary mirror 350 and the inner edge 372 of the front aperture,but without extending that entire length. It may extend from thesecondary mirror 350 towards the primary mirror 360 but without reachingthe inner edge 372 of the front aperture. Similarly, the external sidebaffle 384 may extend from the outer edge 374 of the front aperture, butmay not be long enough to block all direct ray paths through the frontaperture 370 to the image sensor 340. The same is true for the internalside baffle 386. In some cases, there may not be an internal side baffle386 if the oblique extraneous rays are weak or managed by anothermechanism.

The baffles 382, 384, 386 also do not have to have the shapes shown. Forexample, any absorbing structure that extends from the edge of thesecondary mirror 350 to the inner edge 372 of the front aperture withoutblocking the image-forming rays 341 shown in FIG. 3C may serve the samepurpose as the obstruction 382 with the shape shown in FIG. 3. Differentshapes may have advantages in manufacturing or assembly.

As a final set of variations, FIGS. 3B-3C show some situations wherecertain image-forming rays 341 should not be blocked by the baffles.However, this is not strictly required. Blocking some of theimage-forming rays 341 may be acceptable in some designs.

The design of femtoimagers is complicated by constraints such as thevery small volume in which the system must fit, refractive indices ofthe substrate and the surrounding contact lens material, and requiredoptical magnification specifications. The size and curvature of theprimary and secondary mirrors, the size of the image sensor, and theindices of refraction are all examples of parameters that may beadjusted by an optical designer to optimize different design prioritiessuch as optical throughput, depth of focus, field of view, magnificationand resolution.

In some designs, the image sensor 340 is not more than 500 microns wide.For example, the image sensor 340 may be a 500×500 array of sensors,with a sensor-to-sensor pitch of not more than 3 microns and preferablynot more than 1 micron. A 500×500 array with 1 micron pitch isapproximately 500 microns on a side. An array with 500×500 color pixelsusing a Bayer pattern is less than 1 mm on a side using 1 micron pitchindividual sensors (with three or more individual sensors per colorpixel). Image sensors may be other sizes. For example, infrared sensorsmay be significantly larger. Sensor-to-sensor pitches of 10, 20 or even40 microns are possible.

Some designs may have a narrow field of view, such as 2 degrees or less.The two-mirror design shown in FIGS. 3-4 is suited for narrower fieldsof view (for example, in the range of 5 to 15 degrees) andcorrespondingly higher resolutions. Larger and smaller fields of vieware also possible with the two-mirror design.

The specific design of the femtoimager depends on the application. Fornon-imaging applications, the actual resolution may be lower than usedfor imaging applications. For example, a femtoimager with a small number(e.g., 10×10 array) of relatively large pixels may be used as a sensorfor eye tracking applications. The femtoimager may view a far-awayobject, or a closer reference object such as the user's nose.

The design shown in FIGS. 3-4 utilizes a folded optical path. As aresult, the optics have an optical path that is longer than thethickness of the contact lens. This may result in lower aberrations andhigher angular resolutions. The optical path allows the image sensor tobe oriented approximately parallel to, rather than perpendicular to, thecontact lens surfaces. The femtoimager may occupy not more than 1 to 2mm of vertical space (i.e., contact lens thickness) and/or thefemtoimager may have a lateral footprint of not more than 2 to 4 mm².The front aperture may have a maximum lateral dimension of not more than1 to 2 mm.

In addition to capturing images of the external environment or providingeye tracking functionality, femtoimagers may also be used for otherapplications in different types of eye-mounted devices. For example,FIG. 5 shows a cross sectional view of an eye-mounted device with afemtoimager 120 and a femtoprojector 530 (i.e., a small projector alsocontained in the contact lens 110). The femtoimager 120 captures imageswithin its field of view 125. The femtoprojector 530 projects images 595onto the retina 590 of the user. These two may be coordinated so thatthe images captured by the femtoimager are used to determine the images595 projected by the femtoprojector 530.

FIGS. 6-12 show additional variations of the femtoscope of FIG. 3. Thesevariations involve internal refractive interfaces, obscuration positionand shape, and other parameters. The design choices are necessarilyillustrated in combinations and, to keep the number of figures undercontrol, not every possible combination is shown. For example, thechoice of shape of internal refractive interface is largely independentof the choice of obscuration location or obscuration shape. Somecombinations of those choices are illustrated. Those skilled in the artwill appreciate that other, unillustrated combinations may be desirablein certain situations.

The design of FIG. 6 is also based on a transparent substrate 610, withthe image sensor 640 and primary mirror 660 on one face and thesecondary mirror 650 on an opposing face. However, the three-dimensionalobscuration 682 is formed by creating a groove in the core material andthen coating the interior of the groove with an absorbing material. Apartial side baffle 684 is similarly created.

The design of FIG. 7 includes a planarization fill 712. If the corematerial 710 has refractive index n₁, the fill material 712 has adifferent refractive index n₂, and the surrounding material (e.g., thecontact lens material) has refractive index n₃, then there are tworefractive interfaces. The first is at the exit aperture 770. The secondrefractive interface 714 is between the fill material 712 and thesurrounding material. These refractive interfaces may be shaped toachieve various optical functions, for example introducing optical poweror correcting optical aberrations.

In FIG. 2, a femtoimager is shown mounted in a contact lens in a“vertical” configuration. The optical axis and/or axis of symmetry ofthe femtoimager 120 is approximately perpendicular to the outer surfaceof the contact lens 110. In FIG. 8, the femtoimager 820 is mounted in a“horizontal” configuration. The optical axis and/or axis of symmetry ofthe femtoimager optical system 830 is approximately parallel to theouter surface of the contact lens 110. In this configuration, a turningmirror 840 directs image rays from the external environment to thefemtoimager optical system 830.

FIG. 9 shows a cross sectional view of yet another femtoimager in acontact lens 110. The assembly of FIG. 9 has the following structure. Acavity 950 is formed in the contact lens 110 and the solid core 910shown in FIG. 4A is inserted into the cavity 950. In this example, thecavity 950 tapers inwards from the outer surface of the contact lens andthen has straight sidewalls where it contacts the core 910. Thesidewalls of the cavity 950 are absorbing. This may be achieved bycoating the sidewalls of the cavity. Alternatively, a larger hole 940may first be formed and filled with dark colored epoxy 942 (Master BondEP42HT-2MED Black, for example). The cavity 950 is then formed in theepoxy. The remaining dark colored epoxy 942 serves as the absorbing sidebaffle for the femtoimager. Materials other than epoxy may be used. Itssides may be coated instead, for example.

FIG. 10A shows a cross-sectional view of yet another femtoimager, withray paths to the left edge, center and right edge of the image sensor.FIG. 10A is drawn to scale and the femtoscope is approximately 0.7 mm indiameter. In this example, the femtoscope includes a solid, transparentsubstrate 1010 with an annular input aperture 1070 and an outputaperture 1065. The input aperture 1070 is approximately axially alignedwith the convex secondary mirror 1050, and the output aperture 1065 isapproximately axially aligned with the concave primary mirror 1060. Theinput aperture 1070 may form a refractive interface and it may be curvedor otherwise shaped to improve the imaging performance. The inputaperture 1070 and mirrors 1050, 1060 may be aspheric. In this example,the image sensor 1040 is slightly separated from the output aperture1065. Here, the spacing (shown as a rectangle in FIG. 10A) is a gluelayer to attach the image sensor 1040 to the output aperture 1065.

FIG. 10A shows the ray paths for image-forming rays 1041 from the inputaperture 1070 to the image sensor 1040, for rays incident on the leftedge, center and right edge of the image sensor. Image-forming rays fromthe input aperture to other locations on the image sensor will fallwithin the boundaries defined by the rays shown in FIG. 10A. Theaggregate of all image-forming rays may be divided into three raybundles: a first bundle 1041A of image-forming rays propagating from theinput aperture 1070 to the primary mirror 1060, a second ray bundle1041B propagating from the primary mirror 1060 to the secondary mirror1050, and a third ray bundle 1041C propagating from the secondary mirror1050 to the output aperture 1065 (and then on to the image sensor 1040).

In FIG. 10A, there are two spaces between these image-forming raybundles. One space 1078, which will be referred to as the inputinterspace, is located between the first and second ray bundles 1041Aand 1041B. In FIG. 10A, the input interspace 1078 is stippled because itis empty space. There is no material in the input interspace 1078. Theother space 1068, which will be referred to as the output interspace, islocated between the second and third ray bundles 1041B and 1041C. Theoutput interspace 1068 is indicated by the dotted triangle in FIG. 10A.The interior of the triangle is not patterned because the outputinterspace is filled with the substrate material. Baffles may bepositioned in these two interspaces to control extraneous rays withoutinterfering with image-forming rays. For convenience, these will bereferred to as the input baffle and output baffle, respectively. In theexample of FIG. 10A, the input baffle is a groove in the solid substrate1010 with two absorbing surfaces: outer surface 1081A which is adjacentto the first ray bundle 1041A, and inner surface 1081B which is adjacentto the second ray bundle 1041B. The output baffle 1086 is a flatabsorbing ring in this example. It is positioned in the outputinterspace 1068, but does not extend into the interspace as a groovewould. The femtoscope design also includes a side baffle 1089.

FIG. 10B shows operation of the baffle system in blocking extraneousrays. The femtoimager has a field of view and rays within the field ofview are imaged onto the image sensor 1040. Rays outside the field ofview that enter the input aperture 1070 are blocked by the baffles.

Consider first the rays that enter the input aperture 1070 at the outeredge 1074. Refraction at the input aperture is ignored in FIG. 10B forpurposes of illustration. Rays in the bundle 1042 are outside the fieldof view of the femtoimager, and these rays are blocked by the outersurface 1081A of the input baffle. Rays in bundle 1043 are also outsidethe field of view and are blocked by the output baffle 1086. Bundle1041A contains the image-forming rays. Now consider the other extreme ofrays entering the input aperture 1070 at the inner edge 1072. Ray bundle1046 is blocked by the side baffle 1089. Rays in bundle 1041B are theimage-forming rays. FIG. 10B shows rays in the plane of thecross-section. For a femtoscope design that is axially symmetric, skewrays will behave similarly by applying the above analysis to the radialcomponent of each skew ray. Note that all extraneous rays that wouldhave a direct path from the input aperture 1070 to the image sensor 1040are blocked by either the input baffle 1081A or the output baffle 1086.

FIG. 11A shows a cross-sectional view of yet another femtoimager. FIG.11A shows the same set of rays as in FIG. 10A. The femtoscope design inFIG. 11A is the same as in FIG. 10A, except that the output baffle isnot an annular ring. Rather, it is a groove with two absorbing surfaces:outer surface 1186A and inner surface 1186B. As shown in FIG. 11A, thisdesign of the output baffle does not block any of the image-formingrays, so the design is non-vignetting. However, it does block additionalpaths of extraneous rays to the image sensor 1040. Absorbing surfacesare not completely absorbing, so some low fraction of the incident lightwill be reflected off the baffle surfaces. As shown in FIG. 11B,residual reflection of extraneous rays 1142 off the side baffle 1089would be directed to the image sensor 1040. The outer surface 1186A ofthe output baffle blocks these once-reflected extraneous rays 1142 fromreaching the image sensor.

FIG. 12 shows a cross-sectional view of yet another femtoimager thatblocks additional extraneous rays. As shown in FIG. 11B, a small portionof extraneous ray 1143 from outside the field of view may be reflectedby inner surface 1186B to the image sensor 1040. In FIG. 12, the innersurface 1286B of the output baffle is angled to reflect these residualextraneous rays 1143 away from the image sensor 1040 rather than towardsit. The inner surface 1286B of the output baffle may vignette some ofthe image-forming rays.

FIG. 13 shows a cross-sectional view of yet another femtoimager. In FIG.13, the side baffle includes a curved section 1389A, followed by astraight section 1389B. In this design, the curved section 1389A isdefined by an ellipse with two foci 1372 and 1373. The three-dimensionalshape is an elliptical toroid. Focus 1372 is the inner edge of the inputaperture 1070. Focus 1373 is the tip of the outer surface 1286A of theoutput baffle. Every ray that enters the femtoscope through focus 1372and propagates to the elliptical section 1389A is primarily absorbed,but there may be some residual reflection to the other focus 1373. Thisdesign prevents these residual reflections from then propagatingdirectly to the image sensor 1040.

Consider two points along the curved section 1389A as examples. First,ray 1343 enters through focus 1372 and hits the bottom point of theelliptical section 1389A. The non-absorbed portion of ray 1343 isreflected to focus 1373, and the outer surface 1286A of the outputbaffle blocks it from reaching the image sensor 1040. For all other rays1344 that enter through the input aperture 1070 and hit the same bottompoint of section 1389A, reflected light is reflected at a shallowerangle and therefore also will be blocked from reaching the image sensor1040 after only one reflection. The same construction can be made forany other point on the elliptical section 1389A. For example, ray 1345is another ray that enters through focus 1372 and hits the ellipticalsection 1389A somewhere along its length. Reflected light is reflectedto focus 1373. For all other rays 1346 that enter through the inputaperture 1070 and hit the same point on the elliptical section 1389A,reflected light is reflected at a shallower angle and therefore alsowill be blocked from reaching the image sensor 1040 after only onereflection. The straight section 1389B is angled to also preventreflected rays from propagating directly to the image sensor 1040. Theellipse 1389A plus straight section 1389B is just one possible design.Other shapes and curves may also be used to ensure that once-reflectedrays do not have a direct path to the image sensor 1040.

FIGS. 14-15 show cross sectional views of additional femtoimagers. Thesefigures show the use of additional refractive interfaces in thefemtoscope. In both FIGS. 14 and 15, the image-forming rays from thedistant object propagate along optical paths that enter the solidtransparent substrate 1010 with index n₁, reflect off the concave mirror1060, reflect off the convex mirror 1050, and exit the substrate througha central opening (output aperture 1065) to the image sensor 1040. Thefemtoscope operates at near infinite conjugate ratio. The image sensor1040 is close to the output aperture 1065 of the substrate. Thefemtoscope may also contain baffles—input baffles, output baffles and/orside baffles—as described previously.

In FIGS. 14-15, the rays refract at interface(s) before entering thesubstrate 1010, as described in more detail below. In FIG. 14, solidtransparent material 1412 with index n₂≠n₁ creates a first additionalinterface 1472 with the substrate 1010. For example, index n₁ may begreater than 1.5, while index n₂ is less than 1.5. The differencebetween n₁ and n₂ may be greater than 0.1. In FIG. 15, solid transparentmaterial 1512 with index n₃≠n₂ creates a second additional interface1572. These interface(s) may be used to improve the image quality of thefemtoscope.

The use of intermediate material 1412 in FIG. 15 may improve the opticalpower that may be achieved, because the refractive indexes n₁ and n₃ maybe close to each other. The substrate 1010 may have a high index n₁.Index n₃ may also be high in order to match the contact lens material,or it may in fact be the actual contact lens material. Therefore,without an intermediate lower index material, the difference betweenindexes n₁ and n₃ may be low, which would then require a more severelyshaped interface in order to achieve a desired refractive effect.

In FIG. 15, the intermediate material 1412 is introduced and index n₂may be chosen to be significantly lower than both n₁ and n₃ so that theinterfaces 1472, 1572 have more optical power to correct theimage-forming rays. For example, both n₁ and n₃ may be 1.5 or greaterfor the reasons given above. If n₂ is selected to be 1.4 or less, thenthe difference in refractive index at each interface will be at least0.1. In some embodiments, material 1512 may be Zeonex or acrylic andmaterial 1412 may be silicone (PDMS) or low index UV-curable adhesives(e.g. from Norland). Interface 1472 may be concave or convex and isgenerally aspheric. Interface 1572 may be flat or curved. Exit surface1574 may be convex spherical, with radius of curvature similar to thecontact lens or cornea.

The intermediate material 1412 is encapsulated between the substrate1010 and the outer material 1512. It could be something other than asolid, but solid materials have advantages over gases and liquids.Material 1512 interfaces to the rest of the contact lens. In some cases,material 1512 may be the contact lens material, so that exit surface1574 is the exterior surface of the contact lens. If not, material 1512may have the same index as the contact lens material.

In FIG. 15, material 1512 is shaped with a protrusion 1590, as ismaterial 1412 in FIG. 14. The device shown in FIG. 15 is not thefinished optical system. Rather, it is a precursor to the final device.The protrusion 1590 may be used to facilitate handling of the precursorand then removed either before or after assembly into the contact lens.For similar reasons, even if the exit surface 1574 is not the finalexterior surface of the contact lens, it may have the same shape as thefinal surface to facilitate testing of the optical system.

A variety of femtoimager optical systems (femtoscopes) have beendescribed. Each of them may be made small enough to fit in a contactlens using plastic injection molding, diamond turning, photolithographyand etching, or other techniques. Most, but not all, of the systemsinclude a solid cylindrical transparent substrate with a curved primarymirror formed on one end and a secondary mirror formed on the other end.Any of the designs may use light blocking, light-redirecting, absorbingcoatings or other types of baffle structures as needed to reduce straylight.

When a femtoimager optical system is described as “cylindrical”, itscylindrical shape may include a flat on a sidewall. In other words, thecircular cross section of a perfect cylinder is not a requirement, justan overall cylindrical shape. Optical systems may also be made fromextrusions of other shapes, such as triangles, squares, pentagons, etc.

Although the detailed description contains many specifics, these shouldnot be construed as limiting the scope of the invention but merely asillustrating different examples. It should be appreciated that the scopeof the disclosure includes other embodiments not discussed in detailabove. For example, the designs above all use solid substrates, but anair core may also be used. As another example, although the femtoimageris described as embedded in a contact lens, small imaging devices mayalso be used in other applications, such as embedded in an eyeglasseslens, used in endoscopes, or mounted on drones. Various othermodifications, changes and variations which will be apparent to thoseskilled in the art may be made in the arrangement, operation and detailsof the method and apparatus disclosed herein without departing from thespirit and scope as defined in the appended claims. Therefore, the scopeof the invention should be determined by the appended claims and theirlegal equivalents.

What is claimed is:
 1. A femtoscope optical system comprising: a solidtransparent substrate comprised of a transparent first material having arefractive index n₁; a concave mirror positioned to a first side of thesubstrate, the concave mirror having a central opening; a convex mirrorpositioned to a second side of the substrate and opposite the centralopening; a solid transparent second material having a refractive indexn₂, positioned to the second side of the substrate; and a solidtransparent third material having a refractive index n₃, also positionedto the second side of the substrate, the second material positionedbetween the third material and the substrate, the second material andsubstrate forming a first interface with n₂≠n₁, and the third materialand second material forming a second interface with n₃≠n₂; wherein theoptical system projects image-forming rays from a first conjugate to asecond conjugate; and the image-forming rays propagate along opticalpaths that originate from the first conjugate, refract at the secondinterface, refract at the first interface, enter the substrate, reflectoff the concave mirror, reflect off the convex mirror, and exit thesubstrate through the central opening.
 2. The optical system of claim 1wherein the optical system operates at a near infinite conjugate ratio.3. The optical system of claim 1 wherein a distance from the centralopening to the second conjugate is less than a distance from the convexmirror to the central opening.
 4. The optical system of claim 1 whereinn₁−n₂≥0.1 and n₃−n₂≤0.1.
 5. The optical system of claim 1 whereinn₁≥1.50, n₃≥1.50, and n₂≤1.45.
 6. The optical system of claim 1 whereinn₁ and n₃ are closer to each other than to n₂.
 7. The optical system ofclaim 1 wherein the second material comprises silicone.
 8. The opticalsystem of claim 1 wherein the second material comprises an adhesive. 9.The optical system of claim 1 wherein the third material is one ofacrylic or Zeonex.
 10. The optical system of claim 1 wherein the opticalsystem is contained in a contact lens, and the third material is part ofthe contact lens.
 11. The optical system of claim 1 wherein the opticalsystem is contained in a contact lens, and a refractive index of thecontact lens is substantially equal to n₃.
 12. The optical system ofclaim 1 wherein the first interface and the second interface are bothcurved.
 13. The optical system of claim 1 wherein the second interfaceis planar.
 14. The optical system of claim 1 wherein the optical systemis a precursor for assembly into a contact lens, and a surface of thethird material opposite the second interface has a same shape as anexterior surface of the contact lens.
 15. The optical system of claim 1wherein the optical system is a precursor for assembly into a contactlens, and the third material is shaped with a protrusion.
 16. Theoptical system of claim 1 further comprising an input baffle and anoutput baffle.
 17. The optical system of claim 1 wherein the opticalsystem is small enough to be mounted in a contact lens.
 18. The opticalsystem of claim 1 wherein the optical system is small enough to becontained within a 2 mm×2 mm×2 mm volume.
 19. The optical system ofclaim 1 wherein the concave mirror and convex mirror contact thesubstrate.
 20. The optical system of claim 1 wherein the substrate isplastic or glass.